A Unified Framework for Common Knowledge of Rationality with Sets of Probabilities

Studies in Logic, Vol. 14, No. 6 (2021): 68–91   PII: 1674­3202(2021)­06­0068­24

Hailin Liu

Abstract.

The notion of imprecise probability can be viewed as a generalization of the traditional notion of probability. Several theories and models of imprecise probability have been suggested in the literature as more appropriate representations of uncertainty in the context of single­agent decision making. In this paper I investigate the question of how such models can be incorporated into the traditional game­theoretic framework. In the spirit of rationalizability, I present three new solution concepts called Γ-­maximin rationalizability, E-­rationalizability and maximally rationalizability. They are intended to capture the idea that each player models the other players as decision makers who all employ Γ-­maximin, E­-admissibility or maximality as their decision rules. Some properties of these solution concepts such as existence conditions and the relationships with rationalizability are studied.